Finite Group Databasebeta

← C2×#13074298 #14924620

Subgroups — C2×#13074298 #14924620

Order 2816.

3286 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66945C211yesmaximal, characteristic, complemented
3#13074298C2116yesmaximal, direct product factor
4C2×#10622604C211yesmaximal, characteristic, complemented
5C2×#10622844C211yesmaximal, characteristic, complemented
6C2×#10622284C211yesmaximal, characteristic
7C2×#10622601C212yesmaximal, complemented
8C2×#10622283C212yesmaximal, complemented
9C2×#10622603C212yesmaximal, complemented
10C2×#10622278C212yesmaximal, complemented
11C2×#10622261C211yesmaximal, characteristic, complemented
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2212yes—
15C23×D44C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C2×#67000—28no—
20C2×#67000C2218yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66945—28no—
34C2×#66945C2218yescomplemented
35C11×#395C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38#10622844C2218yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42#10622604C2218yescomplemented
43#10622603C22116yescomplemented
44#10622601C22116yescomplemented
45#10622284C2218yes—
46#10622283C22116yescomplemented
47#10622278C22116yescomplemented
48#10622261C2218yescomplemented
49C24×D11C2312yes—
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×D44—28no—
64C22×D44—24no—
65C22×D44—28no—
66C22×D44—44no—
67C22×D44—44no—
68C22×D44C2318yes—
69C22×D44C2314yes—
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11C2314yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—44no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78#67000—232no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11C2314yes—
97C2×C4×Dic11—28no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11D418yescomplemented
100C2×C4×Dic11C2318yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103#66945—232no—
104C11×#95C2314yes—
105C11×#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C2×#2610—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11#4114yes—
123C23×D11C2414yes—
124C23×D11C2412yes—
125C2×Q8×C11—28no—
126C2×Q8×C11—48no—
127C2×Q8×C11—416no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4118yes—
140C22×C4×C11#4114yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C22×Dic11C2412yes—
160C2×D44—216no—
161C2×D44—28no—
162C2×D44—216no—
163C2×D44—48no—
164C2×D44—48no—
165C2×D44—432no—
166C2×D44—416no—
167C2×C4×D11—232no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—48no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181C4⋊Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11—216no—
184C4×Dic11C2×D4116yescomplemented
185C22×#124—111no—
186C22×#117—111no—
187#2610—1116no—
188C2×#395D1111yescharacteristic, complemented
189C2×#394—111no—
190C2×#393—111no—
191C2×#392—111no—
192C2×#390—112no—
193C2×#388—112no—
194C2×#388—112no—
195C2×#386—112no—
196C2×#376—111no—
197C23×C11C22×D412yes—
198C23×C11C2×#4112yes—
199C23×C11C2×#4114yes—
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)14yes—
202C23×C11C2511yescharacteristic
203C22×D11—28no—
204C22×D11—216no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11C2×#4114yes—
227Q8×C11—416no—
228C2×C4×C11—28no—
229C2×C4×C11—28no—
230C2×C4×C11—216no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C2×#4118yes—
245C2×C4×C11C2×#4114yes—
246C2×Dic11—28no—
247C2×Dic11—28no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11C22×D414yes—
259C2×Dic11C22×D414yes—
260D44—432no—
261D44—416no—
262C4×D11—232no—
263C23×Q8C2×D1111yescharacteristic
264C23×D4—112no—
265C23×D4—111no—
266C24×C4—111no—
267C2×#124—118no—
268C2×#124—228no—
269C2×#117—118no—
270C2×#117—228no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C4⋊C4C2×D1112yes—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C42—111no—
283C22×C42—111no—
284C22×C42—112no—
285#395C2×D1118yescomplemented
286#394—118no—
287#393—118no—
288#392—118no—
289#390—1116no—
290#388—1116no—
291#388—1116no—
292#386—1116no—
293#376—118no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1112yes—
299C22×C11#52514yes—
300C22×C11#53214yes—
301C22×C11#53514yes—
302C22×C11#55118yes—
303C22×C11#55518yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C22×#4112yes—
307C22×C11C22×#4111yescharacteristic
308C22×C11C2×H(5,𝔽2)12yes—
309C2×D11—24no—
310C2×D11—28no—
311C2×D11—416no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—816no—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—28no—
326C4×C11—42no—
327C4×C11—44no—
328Dic11—24no—
329Dic11—24no—
330Dic11—42no—
331Dic11—44no—
332C25—111no—
333C25—112no—
334C22×Q8—24no—
335C22×Q8—44no—
336C22×Q8C22×D1114yes—
337C22×D4—118no—
338C22×D4—114no—
339C22×D4—228no—
340C22×D4—224no—
341C22×D4—228no—
342C22×D4—444no—
343C22×D4—444no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—114no—
349C23×C4—224no—
350C23×C4—224no—
351C23×C4—224no—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1112yes—
357#124—2232no—
358#117—2232no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4C22×D1114yes—
364C2×C4⋊C4C22×D1118yes—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—444no—
380C2×C22⋊C4—444no—
381C2×C42—118no—
382C2×C42—114no—
383C2×C42—114no—
384C2×C42—118no—
385C2×C42—224no—
386C2×C42—228no—
387#95—118no—
388#95—114no—
389#95—118no—
390#95C22×D1114yes—
391#95C22×D1118yes—
392C2×C11#261018yescomplemented
393C2×C11C2×#52511yescharacteristic
394C2×C11C2×#53211yescharacteristic
395C2×C11C2×#53511yescharacteristic
396C2×C11C2×#55112yes—
397C2×C11C2×#55512yes—
398D11—44no—
399D11—84no—
400C24—114no—
401C24—112no—
402C24—114no—
403C24—222no—
404C24—224no—
405C24—222no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24—224no—
414C24C23×D1111yescharacteristic
415C2×Q8—28no—
416C2×Q8—48no—
417C2×Q8—416no—
418C2×D4—2216no—
419C2×D4—228no—
420C2×D4—2216no—
421C2×D4—448no—
422C2×D4—448no—
423C2×D4—4432no—
424C2×D4—4416no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—112no—
441C22×C4—228no—
442C22×C4—228no—
443C22×C4—2232no—
444C22×C4—224no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—228no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4D4×D1114yes—
454C22×C4#434318yes—
455C22×C4#434314yes—
456C22×C4C23×D1114yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1114yes—
460C22×C4C23×D1112yes—
461C4⋊C4—28no—
462C4⋊C4—48no—
463C4⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—2216no—
466C22⋊C4—2216no—
467C22⋊C4—228no—
468C22⋊C4—2216no—
469C22⋊C4—2216no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C42—1116no—
473C42—228no—
474C42—2216no—
475C11C2×#261011yescharacteristic, complemented, Sylow
476C23—114no—
477C23—228no—
478C23—2216no—
479C23—222no—
480C23—224no—
481C23—222no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—444no—
491C23—448no—
492C23—444no—
493C23—448no—
494C23—448no—
495C23—448no—
496C23—448no—
497C23—448no—
498C23—448no—
499C23—448no—
500C23C2×D4×D1112yes—
501C23#6703714yes—
502C23C2×#434314yes—
503C23C2×#434312yes—
504C23#41×D1112yes—
505C23C24×D1111yescharacteristic
506Q8—416no—
507D4—4432no—
508D4—4416no—
509C2×C4—28no—
510C2×C4—28no—
511C2×C4—216no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—44no—
523C2×C4—48no—
524C2×C4—114no—
525C2×C4—114no—
526C2×C4—2232no—
527C2×C4—228no—
528C2×C4—228no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—444no—
538C2×C4—448no—
539C2×C4C2×D4×D1114yes—
540C2×C4C2×#434318yes—
541C2×C4C2×#434314yes—
542C22—228no—
543C22—224no—
544C22—442no—
545C22—444no—
546C22—442no—
547C22—4416no—
548C22—444no—
549C22—444no—
550C22—444no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—444no—
555C22—8816no—
556C22#1062312314yes—
557C22#1062315814yes—
558C22#1062316818yes—
559C22#1062325614yes—
560C22#1062326518yes—
561C22C22×D4×D1111yescharacteristic
562C22C2×#6703712yes—
563C22C22×#434312yes—
564C22C22×#434311yescharacteristic
565C22C2×#41×D1111yescharacteristic
566C4—28no—
567C4—24no—
568C4—24no—
569C4—44no—
570C4—42no—
571C4—224no—
572C4—224no—
573C4—442no—
574C4—444no—
575C2—444no—
576C2—884no—
577C2#1307429818yesdirect product factor
578C2C2×#1062315811yescharacteristic
579C2C2×#1062325611yescharacteristic
580C2C2×#1062312311yescharacteristic
581C2C2×#1062316812yes—
582C2C2×#1062326512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#395D11
hypocenterC11C2×#2610
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66945C2semidirect
3. #13074298C2direct (N × H)
4. C2×#10622604C2semidirect
5. C2×#10622844C2semidirect
7. C2×#10622601C2semidirect
8. C2×#10622283C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622261C2semidirect
12. C2×C11×#395C2semidirect
20. C2×#67000C22semidirect
34. C2×#66945C22semidirect
35. C11×#395C22semidirect
38. #10622844C22semidirect
42. #10622604C22semidirect
43. #10622603C22semidirect
44. #10622601C22semidirect
46. #10622283C22semidirect
47. #10622278C22semidirect
48. #10622261C22semidirect
99. C2×C4×Dic11D4semidirect
184. C4×Dic11C2×D4semidirect
188. C2×#395D11semidirect
285. #395C2×D11semidirect
392. C2×C11#2610semidirect
475. C11C2×#2610semidirect
577. C2#13074298direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#670002
C22×#669452
#130742982
C2×#106226042
C2×#106228442
C2×#106222842
C2×#106226012
C2×#106222832
C2×#106226032
C2×#106222782
C2×#106222612
C2×C11×#3952
C2×#261011